Math Problem Statement

1 1/5 ÷ 3/4 =

Solution

To solve 115÷341 \frac{1}{5} \div \frac{3}{4}, we follow these steps:

  1. Convert the mixed number 1151 \frac{1}{5} into an improper fraction: 115=651 \frac{1}{5} = \frac{6}{5}

  2. Now, divide 65\frac{6}{5} by 34\frac{3}{4}, which is the same as multiplying by the reciprocal of 34\frac{3}{4}: 65÷34=65×43\frac{6}{5} \div \frac{3}{4} = \frac{6}{5} \times \frac{4}{3}

  3. Multiply the numerators and the denominators: 6×45×3=2415\frac{6 \times 4}{5 \times 3} = \frac{24}{15}

  4. Simplify 2415\frac{24}{15} by dividing both the numerator and the denominator by their greatest common divisor, which is 3: 2415=85\frac{24}{15} = \frac{8}{5}

So, the result is 85\frac{8}{5}, which can also be written as 1351 \frac{3}{5}.

Would you like more details on any of these steps?


Here are some related questions to think about:

  1. How do you multiply fractions?
  2. What is the process to convert improper fractions into mixed numbers?
  3. How do you simplify fractions?
  4. How do you divide fractions without converting them into decimals?
  5. Why is dividing by a fraction equivalent to multiplying by its reciprocal?

Tip: Always simplify fractions at the end to get the most reduced form.

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Math Problem Analysis

Mathematical Concepts

Fractions
Division
Mixed Numbers
Improper Fractions

Formulas

Reciprocal of a Fraction
Multiplication of Fractions
Simplification of Fractions

Theorems

Reciprocal Theorem

Suitable Grade Level

Grades 6-8